This O'Reilly book by Danny Goodman is an excellent compendium of real-world problems and solutions. We know this book is worth your time because Dori was one of the book's technical reviewers.
Ajax in Action
Head Rush Ajax
This is a very readable and even fun introduction to Ajax by Brett McLaughlin. The Head First and Head Rush series style is to use lots of visuals, repetition, and humor to get past their possibly dry subjects, and applying this to Ajax works well. It's another O'Reilly Media book.